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Proof step 6 from proof div-minus-onediff (previous step)

0 < j, i0 * j + j0 < 0, i0 < j, i0 < j + j0, j0 < 0, 0 < j + j0, i0 ≤ 0 ⊦ i0 = ((i0 * j + j0) + 1 - j) / j + 1, j0 = 0

User applied rule cut formula

And obtained the following new goals

Proof step 7:
(i0 * j + j0) + 1 - j = j * (i0 - 1) + j0 + 1, 0 < j + j0, j0 < 0, i0 < j + j0, i0 < j, i0 * j + j0 < 0, 0 < j, i0 ≤ 0 ⊦ i0 = ((i0 * j + j0) + 1 - j) / j + 1, j0 = 0

Rule argument

fma: (i0 * j + j0) + 1 - j = j * (i0 - 1) + j0 + 1

Additional information

Used simplifier rules: ⊦ i - j = i0 ↔ i = i0 + j; (s)% ⊦ i * j + i = i * (j + 1); (s)% ⊦ i + (j - i) = j; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i + j = i + i0 ↔ j = i0; (s) Used formulas: (i0 * j + j0) + 1 - j = j * (i0 - 1) + j0 + 1